Improved cantilever profiles for sensor elements

Abstract

The problem of simultaneously enhancing sensitivity and noise immunity of microcantilevers is investigated. The dependence of deflection and resonant frequency of a microcantilever on its dimensions is studied. A principle to increase deflection and resonant frequency simultaneously is established. Several cantilevers agreeing with this principle are investigated using analytical models and are compared with FEM simulations. Using these results, a cantilever profile that achieves a larger deflection and a larger resonant frequency compared with uniform cantilevers is proposed to be used in sensor elements.

Customized silicon cantilevers for Casimir force experiments using focused ion beam milling

“…In fact if a different theoretical model is used, the cantilevers theoretical characteristics might be different from the ones resulting from equations (4) and (5), changing the expected cantilever's minimum force. This is indeed the case for non-prismatic cantilevers [23].…”

Geometry and Profile Modification of Microcantilevers for Sensitivity Enhancement in Sensing Applications

“…Thickness is another parameter that affects the cantilever frequency whose increase makes the frequency acutely increase, but thickness has no effect on the frequency shift of the prismatic cantilever according to Eq. (12). Thus, it is beneficial for the prismatic microcantilevers to reduce the mass near the free end by increasing the taper ratio.…”

“…Zhang et al (11) obtained the fundamental resonant frequencies of microcantilevers with various linear geometries by using the variational method but did not consider the effect of the active sensing area. The frequency properties of microcantilevers with varying profiles were also investigated by Fernando et al (12) The very essence of modifying the geometry or profile is to improve the weight distribution of microcantilevers, which is a beneficial scheme for microcantilever design. However, little work that discusses the improvement of the microcantilever weight distribution by changing both the geometry and profile of the microcantilever has been reported to the best of our knowledge.…”

Deflection, Frequency, and Stress Characteristics of Rectangular, Triangular, and Step Profile Microcantilevers for Biosensors

“…The Stoney Equation for a triangular profile cantilever can be given as [10]: $\mathrm{\Delta }z= \frac{8 (1-\nu ) \mathrm{\Delta }\sigma l^2}{E{(t_0-t_{\mathrm{l}})}^2}\left[\text{ln}\left(\frac{t_0}{t_{\mathrm{normall}}}\right)+\frac{t_{\mathrm{normall}}}{t_0}-1\right]$where t 0 and t l are the thicknesses of the cantilever at the fixed and free ends. Hoffman and Wertheimer [22] gave a simple and accurate formula for calculating the fundamental resonant frequency for a beam of triangular profile: $f_0= C\sqrt{\frac{S}{M}}$where S and M are spring constant and mass of the cantilever; and C is taper-ratio dependent mass distribution parameter.…”